Article

    Ufa Mathematical Journal
    Volume 7, Number 2, pp. 33-54

    Initial length scale estimate for waveguides with some random singular potentials


    Borisov D.I., Karimov R.Kh., Sharapov T.F.

    DOI:10.13108/2015-7-2-33

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    In this work we consider three examples of random singular perturbations in multi-dimensional models of waveguides. These perturbations are described by a large potential supported on a set of a small measure, by a compactly supported fast oscillating potential, and by a delta-potential. In all cases we prove initial length scale estimate.